Convergent Series

A convergent series is an infinite sum of numbers where the total approaches a specific finite value as more terms are added. Imagine adding smaller and smaller amounts each time; if these amounts decrease quickly enough, the total sum will settle at a particular number rather than growing without bound. For example, the series 1/2 + 1/4 + 1/8 + 1/16 + ... converges to 1. In essence, convergence means that even though there are infinitely many terms, their combined sum stabilizes to a fixed point.